is it so the digest challenge wouldn't provide any additional security over the form based authentication?
It's actually the other way around: HTTP digest auth requires the server to store all passwords in it's database in plaintext or weakly hashed (e.g. MD5), because it needs to be able to calculate a digest on them. With Basic auth it's possible to store passwords in strongly hashed form (e.g. scrypt), so Basic auth is more secure (in the presence of TLS of course).
Why doesn't the form based authentication on web browsers use the digest scheme instead?
Form-based authentication isn't really a standard, it's just an approach in which the user is typically presented with a username and password HTML form fields and a Submit button, which triggers the submission of form data to the server via an HTTP POST. That's how HTML forms normally work.
However, you're free to augment this process any way you want, since it's possible to intercept button clicks in JavaScript and completely bypass the form submission. For example, you can implement digest-based authentication via Ajax (e.g. digest-ajax), as well as client-side PBKDF2, bcrypt, scrypt, or really anything else.
In which context would the digest based scheme actually be more secure than plain text over a secure channel?
It's more secure when for example using a proxy, because the proxy gets to see a digest instead of a plaintext password, thus making it possible to potentially even use a public proxy.
